Algebraic Informatics. 9th International Conference, CAI 2022 Virtual Event, October 27–29, 2022 Proceedings

Preface
Organization
Abstracts of Invited Talks
	Weighted Automata Over Monotonic Strong Bimonoids: Decidability and Undecidability of Finite Image
	Constraints, Graphs, Algebra, Logic, and Complexity
	Contents
Invited Papers
Chaining Multiplications in Finite Fields with Chudnovsky-Type Algorithms and Tensor Rank of the k-Multiplication
	1 Introduction
		1.1 Context, Notation and Basic Results
		1.2 New Results and Organisation
	2 Theoretical Construction of a Multiplying Algorithm
		2.1 Notations
		2.2 Algorithm
	3 On the Existence of These Algorithms
		3.1 Strategy of Construction
		3.2 Towers of Algebraic Function Fields
	4 Uniform Upper Bounds
	References
On Some Algebraic Ways to Calculate Zeros of the Riemann Zeta Function
	1 The Riemann Hypothesis
	2 The Riemann Hypothesis in the Arithmetical Hierarchy
	3 Calculation of the Zeta Zeros by Solving Algebraic Equations
	4 Calculation of Summands from Dirichlet Series for the Zeta Function at Its Zeros
	References
Shuffle Product of Regular Languages: Results and Open Problems
	1 Introduction
	2 Shuffle and Recognition
		2.1 Shuffle Product
		2.2 Monoids and Ordered Monoids
		2.3 Power Monoids and Lower Set Monoids
	3 Classes of Languages Closed Under Shuffle
		3.1 Varieties of Languages Closed Under Shuffle
		3.2 Positive Varieties of Languages Closed Under Shuffle
		3.3 Intermixed Languages
	4 Sequential and Parallel Decompositions
		4.1 Definitions and Examples
		4.2 Closure Properties
		4.3 Schnoebelen's Problem
	5 Conclusion
	References
Contributed Papers
Ordering the Boolean Cube Vectors by Their Weights and with Minimal Change
	1 Introduction
	2 Basic Notions and Preliminary Results
	3 Ordering the Vectors of the Boolean Cube by Their Weights and with Minimal Change
	4 Algorithm for Generating the Vectors of the Boolean Cube Ordered by Weights and with Minimal Change
	5 Conclusions
	References
Designated-Verifier Linkable Ring Signatures with Unconditional Anonymity
	1 Introduction
	2 Preliminaries
		2.1 Notation
		2.2 Security Assumptions
	3 UDVLRS Definition and Security Model
		3.1 UDVLRS Definition
		3.2 Correctness
		3.3 Adversarial Capabilities
		3.4 Unforgeability
		3.5 Anonymity
		3.6 Non-transferability
		3.7 Linkability
		3.8 Non-slanderability
	4 Our Construction
	5 Security Analysis
	6 Conclusion and Future Work
	References
Finding Points on Elliptic Curves with Coppersmith's Method
	1 Introduction
	2 Preliminaries
		2.1 Some ECC Cryptosystems
		2.2 Lattice Basis Reduction and Coppersmith's Method
	3 Small Solutions of the Elliptic Curve Equation
	4 A Numerical Example
	5 Conclusion
	References
Weighted Propositional Configuration Logic over De Morgan Algebras
	1 Introduction
	2 Related Work
	3 Preliminaries
	4 Unweighted PCL
	5 Weighted PCL over De Morgan Algebras
	6 Examples
	7 Discussion
	8 Conclusion
	References
Weighted Two-Way Transducers
	1 Introduction
	2 Preliminaries
	3 Weighted Two-Way Transducers
	4 Relation to Unweighted Case
	5 Closure Properties
	References
A Formal Algebraic Approach for the Quantitative Modeling of Connectors in Architectures
	1 Introduction
	2 Related Work
	3 Preliminaries
	4 The Weighted Algebra of Interactions
	5 The Weighted Algebra of Connectors
	6 On Congruence Relation for Fusion-wAC(P) Connectors
	7 Discussion
	8 Conclusion
	References
Watson-Crick Powers of a Word
	1 Introduction
	2 Preliminaries
	3 A Binary Operation Generating Watson-Crick Powers
	4 Watson-Crick Conjugate Equations
	5 Conjugacy and Commutativity with Respect to
	6 -Primitive Words, and a Word's -Primitive Root Pair
	7 Conclusions
	References
A Normal Form for Matrix Multiplication Schemes
	1 Introduction
	2 Matrix Multiplication Schemes
	3 The Symmetry Group
	4 Minimal Orbit Elements
	5 Minimizing the First Row
	6 Timings and Analysis
	References
Bideterministic Weighted Automata
	1 Introduction
	2 Preliminaries
	3 Bideterministic Weighted Automata over a Semiring
	4 The Minimality Property of Bideterministic Automata
		4.1 Fields and Integral Domains
		4.2 Other Commutative Rings
		4.3 Positive Semirings
	5 Decidability of Bideterminisability
		5.1 Fields
		5.2 Tropical Semirings
	References
How to Decide Functionality of Compositions of Top-Down Tree Transducers
	1 Introduction
	2 Top-Down Tree Transducers
	3 Functionality of Two-Fold Compositions
		3.1 Construction of the LA-Transducer M
		3.2 Correctness of the LA-Transducer M
		3.3 Functionality of Arbitrary Compositions
	4 Conclusion
	References
Computation of Solutions to Certain Nonlinear Systems of Fuzzy Relation Inequations
	1 Introduction
	2 Preliminaries
	3 Certain Types of Fuzzy Relation Inequations and Their Solutions
	References
When Variable-Length Codes Meet the Field of Error Detection
	1 Introduction
	2 Preliminaries
	3 Error Detection and the Prefix Metric
	4 Error Detection and the Factor Metric
	5 Error Detection in the Topologies Associated to (anti-)automorphisms
	6 Concluding Remark
	References
Author Index